SAG: Wall-Crossing for K-theoretic Invariants via Non-Abelian LocalizationSeminar Algebraic Geometry (SAG)

by Miguel Moreira

Thursday Jan 8, 2026, 10:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

An important question with many practical applications in enumerative geometry is to understand how invariants attached to moduli spaces of sheaves/complexes/quiver representations change when we vary the stability condition. Wall-crossing for motivic invariants has been a central tool in Donaldson-Thomas theory of Calabi--Yau 3-folds. In a non-CY setting, more recently, Joyce developed a wall-crossing framework for cohomological invariants and Liu adapted his ideas to K-theoretic invariants. In this talk, I will explain a new approach to such wall-crossing formulas and an alternative way to define enumerative invariants in the presence of strictly semistable objects. This new framework extends the range of wall-crossing formulas we can prove, allowing us to deal for example with objects in the derived category of sheaves. This is joint work with Ivan Karpov.